Fig. REF  displays these quantities, calculated in the covariant approach with the DD-ME2 [1]} EDF, during the alpha emission of \(^{212}\) Po. They are taken along the least action path determined in [2]}, leading to the emission of an alpha-particle by the \(^{212}\) Po nucleus. Let us recall, from the discussion in section II, that the NLF is sensitive to the pure spatial overlap of the nucleons (n\(\uparrow \) ,n\(\downarrow \) ,p\(\uparrow \) ,n\(\downarrow \) ), which is a necessary (but not sufficient) condition for
alpha preformation. The information of compactness and on the binding of this 4 nucleons state, is brought by the study of the density, namely localized cluster at about the saturation density. On Fig. REF , the NLF indicates that there is a pure 4-nucleons overlap (\(C_{q\sigma }=1\) , in inset \(c\) ), before the alpha-particle is fully formed in the density (inset \(f\) ), where the number of nucleons is 4. This could be interpreted as the first step of alpha emission: the 4 nucleons first overlap in a delocalized state (inset c). This may be a necessary step of alpha-particle preformation. Later, during the emission process, the alpha-particle gets formed as a cluster (i.e. spatially localized with 4 nucleons at saturation density, inset f) in a second step. It should be noted that in this last case, the alpha cluster in the density coincides with a NLF value C\(_{q\sigma }\) =1, showing that it is a totally pure
4 nucleon overlap. The present analysis enlightens the mechanism of the alpha formation process during the alpha decay: within the present approach, the alpha-particle starts to be preformed in a delocalized 4 nucleons state, and along the process, the density probability increases, so to end as a localized alpha-particle, namely a cluster, as expected in the RMF case.
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